Optimization of Transmission Conditions in Waveform Relaxation Techniques for RC Circuits

Waveform relaxation techniques have become increasingly important with the wide availability of parallel computers with a large number of processors. A limiting factor for classical waveform relaxation, however, is the convergence speed for an important class of problems, especially if long time windows are considered. In contrast, the optimized waveform relaxation algorithm discussed in this paper is well suited to address this problem. Today several numerical analyses have shown that optimized waveform relaxation algorithms can overcome slow convergence over long time windows. However, the optimized waveform relaxation techniques require the determination of optimized parameters. In this paper, we present a theoretical foundation for the determination of the optimized parameters for an important class of RC circuits.